Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #11718364 | C2 | direct (N × H) |
| 72. C2×C13 | #491 | semidirect |
| 90. C13 | C2×#491 | semidirect |
| 112. C2 | #11718364 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88124 | 2 |
| C2×#88123 | 2 |
| C2×C13×#97 | 2 |
| C2×#88056 | 2 |
| #11718364 | 2 |
| C2×#491 | 13 |